Electrical network



June 3,1930. 0. J; ZOBEL 1,760,973

ELECTRICAL NETWORK Filed March 27, 1928 2 Sheets-Sheet l brqvedaiwe (okra us) IQ Q Q Q g 9 E-equemy (cycles per second 1000 20m 3000 4000 .5000

INVENTOR OJZoeL BY ATTORNEY June 3, 1930. o. J. ZOBEL ELECTRICAL NETWORK Filed March 27, 1928 2 Sheets-Sheet 2 (smmppzu INVENTOR BY OJZoel 7 ATTORNEY Patented June 3, 1930 UNITED STATES PA ENT oFFIc-E Y OTTO J. ZOIBEL, OF

NEW-YORK, N. Y., ASSIGNOR TO AMERICAH TELEPHONE AND TELE- GRAPH COMPANY, A CORPORATION .OIENEW YORK ELEcTRicAL NETWORK Application filed March 21, 1928. Serial a... 265,200.

late an extended electrical transmission circuit, or other transducer. Another object of my invention is to provide a compact network that shall accurately simulate a smooth line of a certain length. Still another object of my invention is to provide a network of fixed general pattern with certain parameters capable of determination or adjustment to make the network simulate accurately a transmis' sion line of known properties. These objects and various other objects of my invention will become apparent on consideration of an example of'practice according to the invention which I will disclose in the following specification taken with the accompanying drawings. It' will be understood that this .specification relates principally to this particular example of the invention, and that its scope will be indicated in the appended claims.

Referring to the drawings, Figure 1 is a diagram of my network with the impedances shown in generalized symbols; Fig. 2 is a diagram with the impedances shown more specifically; and Figs. 3 and 4 are characteristic diagrams showing the properties of this network over a certain range of frequencies.

It is desired to construct a network that shall simulate a smooth transmission line of length Z, propagation constant characteris tic impedance 70, series impedance 2,, and shunt impedance 2 these impedance values being for the line as a whole.

It' is known that for a smooth line the square of the propagation constant is equal to the product of the series impedance by the shunt admittance, and that the square of the characteristic impedance is equal to the quotient of the seriesimpeda'nce divided by the shunt admittance, such impedance and such admittance being taken per unit length of the line. See, for example, J. A. Flemings book The Propagation of Electric Currents in Telephone and Telegraph Conductors, third edition, 1919, page 84. From these properties it ca that for this smooth line It lz z (2) and Let X the open circuit impedance of this smoth line section, and let Y=its short-circult impedance. Then it can readily be proved that These results can be obtained by the aid of and n readily be deduced V formula. 61 on page 99 of Flemings book,

above referred to.

From Equations readily that (3) and l), it follows and Thus, a, and 2,, are inverse networks of impedance product In. In a physical smooth line, a, is simulated by series resistance and inductance, and z by parallel resistance and capacity (assuming the line constants to be independent of frequency), both represented by simple physical networks. In other cases, they may be realized in desired frequency ranges, more or less approximately, by physical networks. It will be assumed 1n what follows that 2, 2 are given by the foregoing Equations and (6).

The structure which is to simulate the smooth line consists of a finite number of lattice network sections, as shown in Fig. 1. In this particular illustrative example, the number of these sections is taken at two. It

. will be seen that in each section certain multo obtain more definite values for the ms based on the assumption that the simulation is to be accurate only for moderate propagation lengths yl.

5 Let a equal twice the impedance of the parallel combination in Fig. 1, m e and 1 2 then 1 I 1/2m z,,+m /2z, (7) In a sequence of like lattice networks, the characteristic impedance is given by wherein for each section 2 /2 represents the series impedance in each of two non-adjacent sides, and 22 represents the lattice im- 2o pedance in each of the remaining two non-adjacent sides. To satisfy the condition for the desired characteristic impedance at all frequence's, we should have and, accordingly, it follows that Regardingthe second and third members of the foregoing equation as a qu'adratic with e as the unknown cordingly,' and su stitutingfrom Equation (8 the result is obtained that Y 1+z"/2K is obtained that uantity and Solving c; These four Equations (19) involve the four Substituting in Equation 12 from E mi- 1 The foregoing result is for the first section of Fig. 1. By a similar'procedure, the following equation is obtained for the second section of that figure,

It remains to choose the ms so that for moderate propagation lengths, y=yl, the composite network will give I approximately=y= Z 17 ;At this point, I shall introduce an important simpllfication by utilizing the following identity' Comparing Equations (16) and (18), it will 10 at once be seen that for small values of y, we can satisfy Equation (17) if we identify the coeflicients of powers of gin equation (16) as follows:

l a 'i e '1 z g ms as unknown quantifies "Byl elimination, the following sixth degree equation is obtainedform z i e/ 1 m/ "e/6 obtaine I Of the real positive roots of Equation the following is found as suitable for our procedure From this, by the aid of Equations (20) and (21 the values for the remaining ms are as follows:

m. =0.144.5e m'.=0.0426a (23) m' =0.92403 propagation characteristic from the smooth line value also increases, but it amounts to less than 1.41% even atly 3.0; this may be inferred from a comparison of Equations (16) and (18).

Further to illustrate my invention, the foregoing results wereapplied in the case of a lO l-mil open wire smooth line having the constants per loop mile (for wet weather, and assumed independent of frequency) R=10.12 ohms L=3.66 mh.

G=3.20 micromhos (24) O=0.00837 m where R, L, G and G stand, respectlvely, for series resistance, series inductance, shunt conductance and shunt capacity per loop mile. The corresponding network for a length Z is shown in Fig. 2. The values of 1ts elements are determined by comparison with Fig. 1, taking the values of the ms found above, and observingthat More particularly, the values of the resis tances, inductances and capacities in Fig. 2 are as follows, expressed in terms of Equations (22), (23) and (2 1); Y

With those This simulation For example, if the 2-section network here considered is equivalent to 20 miles of smooth line then two such 2-section networks in tandem would be equivalent to 40 miles of such smooth line.

While I have exemplified my invention for simulating a smooth line of moderate length, it will be apparent that the same procedure will applying in the case of any symmetrical general section of any passive transducer where .2 and a are determlned from the open circuit and short circuit impedances, X and Y, of the section and can be simulated in the desired frequency range by simple physical elements.

In the following claims I use the term multiple to include sub-multiple, unless expressly stated otherwise, i. e., 1 use multiple to mean a factor less than unity as well as greater than unity.

I claim:

1. A smooth line having a certain series impedance and a certain shunt impedance and a network associated therewith andsimulating it, said network comprising a plurality in each of its arms, these last mentioned impedances' being respectively real number multiples of said series impedance and shunt impedance. 7 i

2. A smooth line having a certain series impedance and a certain shunt impedance and a network associated therewith and simulating, it, said network comprising a plurality of lattice sections each with impedances'in its arms, each such impedance being a real number multiple of oneof said first mentioned series and shunt impedances.

3. A smooth line of series impedance 2. and shunt impedance 2 and a network of several lattice sections associated therewith and'simulating it, one pair of non-adjacent arms of one section each having the admittance value 1/m z +m /z and the other pair each having the impedance value m z +z /m where the ms are determinate real number constants'."

4, A network of several lattice sections to simulate a smooth line of series impedance 2,, and shunt impedance 2 one pair of non-adjacent arms of one section each having the L admittance value 1/m z +m /z and the other pair each having the impedance value m z +z /m where, for one section,"m 0.457 37 and m =0.14456, and for another sec tion, m' =0.04263' and m' =0.92403.

In testimony whereof, I have signed my name to this specification this 24th day of March, 1928.

' OTTO J. ZQBEL.

90 of lattice sections each with two impedances 

